The Method of Characteristics

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The Method of Characteristics

• Solving IVPs the Easy Way

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IVP Equation IC
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Motivation
in space such that
Try to find a curve
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The General Case
Parametrize a curve
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Solve
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Solve
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Solve
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Invert
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Our Solution is
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An Easy Example
Parametrize a curve
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Solve
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Solve
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Solve
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Invert
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Our Solution is
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Another Example
Parametrize a curve
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Solve
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Solve
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Solve
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Invert
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Our Solution is
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Important Points

• Its so easy

• Method generalizes to solve most any first order
  PDE

• This method fails when we cannot invert the
  variables

• A major application follows

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How to Destroy a PlanetBy Andrew
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How to Destroy a Planet

• Decide on a planet

• Isolate

• Aim

• Fire

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How to Destroy a Planet

• Decide on a planet
• Isolate planet
• Aim
• Fire